Gradient corrections for reference dosimetry using Farmer-type ionization chambers in single-layer scanned proton fields

The local depth dose gradient and the displacement correction factor for Farmer-type ionization chambers are quantified for reference dosimetry at shallow depth in single-layer scanned proton fields.

Integrated radial profiles as a function of depth (IRPDs) measured at three proton therapy centers were smoothed by polynomial fits. The local relative depth dose gradient at measurement depths from 1 to 5 cm were derived from the derivatives of those fits. To calculate displacement correction factors, the best estimate of the effective point of measurement was derived from reviewing experimental and theoretical determinations reported in the literature. Displacement correction factors for the use of Farmer-type ionization chambers with their reference point (at the center of the cavity volume) positioned at the measurement depth were derived as a ratio of IRPD values at the measurement depth and at the effective point of measurement.

Depth dose gradients are as low as 0.1-0.4% per mm at measurement depths from 1 to 5 cm in the highest clinical proton energies (with residual ranges higher than 15 cm) and increase to 1% per mm at a residual range of 4 cm and become larger than 3% per mm for residual ranges lower than 2 cm. The literature review shows that the effective point of measurement of Farmer-type ionization chambers is, similarly as for carbon ion beams, located 0.75 times the cavity radius closer to the beam origin as the center of the cavity. If a maximum displacement correction of 2% is deemed acceptable to be included in calculated beam quality correction factors, Farmer-type ICs can be used at measurements depths from 1 to 5 cm for which the residual range is 4 cm or larger. If one wants to use the same beam quality correction factors as applicable to the conventional measurement point for scattered beams, located at the center of the SOBP, the relative standard uncertainty on the assumption that the displacement correction factor is unity can be kept below 0.5% for measurement depths of at least 2 cm and for residual ranges of 15 cm or higher.

The literature review confirmed that for proton beams the effective point of measurement of Farmer-type ionization chambers is located 0.75 times the cavity radius closer to the beam origin as the center of the cavity. Based on the findings in this work, three options can be recommended for reference dosimetry of scanned proton beams using Farmer-type ionization chambers: (a) positioning the effective point of measurement at the measurement depth, (b) positioning the reference point at the measurement depth and applying a displacement correction factor, and (c) positioning the reference point at the measurement depth without applying a displacement correction factor. Based on limiting the acceptable uncertainty on the gradient correction factor to 0.5% and the maximum deviation of the displacement perturbation correction factor from unity to 2%, the first two options can be allowed for residual ranges of at least 4 cm while the third option only for residual ranges of at least 15 cm.